7x+1y−5=0
y=-7x+5
so the distance minimum will be on a line thru the point (-2,6) and has a slope of 1/7

y=1/7 x+b
-2=1/7 (-2)+b
b=-2+2/7

now look at the lines to find the intersection.
y=-7x+5
y=x/7 -2+2/7
set them equal
-7x+5=x/7-2+2/7
solve for x, then go back and solve for y. That (x,y) is the point on the original line which is closest to (-2,-6)

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